Question

the greatest value of the function is - 5 sin theta + 12 cos theta is ​

Answer 1

Answer:In general, the smallest & the greatest values of asinθ+bcosθ is given as

−a2+b2−−−−−−√≤asinθ+bcosθ≤a2+b2−−−−−−√

setting the corresponding values in above general formula,

−(−5)2+122−−−−−−−−−−√≤−5sinθ+12cosθ≤(−5)2+122−−−−−−−−−−√

−13≤−5sinθ+12cosθ≤13

∴ Max.(−5sinθ+12cosθ)=13